BUCKLING ANALYSIS OF VARIABLE ANGLE TOW, VARIABLE THICKNESS PANELS WITH TRANSVERSE SHEAR EFFECTS

摘要

The idea of tailoring the structural performance of composite laminates by spatially varying the point-wise fibre orientations over the planform has been explored since the early 1990's. For example, the work by Hyer & Lee [1] and Hyer & Charette [2] showed that such variable angle tow (VAT) laminates can improve the stress concentration around holes by arranging the fibres in the direction of load paths. In recent years the use of fibre re-inforced composites in primary aircraft structures has led to increased interest in VAT technology. Numerous works have shown that tailoring the in-plane stiffness of a plate allows prebuckling stresses to be re-distributed to supported regions and thereby improve the buckling behaviour [3-7]. In this manner VAT technology has been shown to improve the buckling performance of a composite fuselage window section by 12% compared to an equivalent straight-fibre laminate [8] and alleviate the pressure pillowing of fuselage sections [9]. Recent results by Wu et al. [10] show that VAT plates with linear fibre variations can be designed to exhibit smaller stiffness reductions in the post-buckling regime than their straight-fibre counterparts. What is more, the optimum fibre orientations for increasing the buckling load are similar to those for minimising the transverse displacement in the post-buckling regime [11]. Currently the major technology for manufacturing VAT laminates is the automated fibre placement (AFP) technique develeoped in the 1980's. AFP uses a robotic fibre placement head that deposits multiple pre-impregnated tows of "slit-tape" allowing cutting, clamping and restarting of every single tow. While the robotic head follows a specific fibre path, tows are heated shortly before deposition and then compacted onto the substrate using a special roller. Due to the high fidelity of current robot technology AFP machines can provide high productivity and handle compex geometries [12]. However, AFP steers tows by bending the fibres causing local fibre buckling on the inside radii of the curved tow, consequently limiting the steering radius of curvature [13]. Furthermore, if individual tows are placed next to each other by shifting the reference path along a specific direction, tow gaps and overlaps are inevitably required to cover the whole surface. To overcome the drawbacks of AFP the continuous tow shearing technique (CTS) was developed which uses shear deformation to steer fibres at the point of application [14]. This technique not only allows much tighter radii of curvature but tow gaps and overlaps are also avoided by tessalating tows on the substrate [14]. One of the drawbacks of CTS is that in order to maintain the volume fraction of fibre the thickness of a tow inherently increases as it is sheared. The relation between unsheared tow thickness to and sheared tow thickness t_θ is, t_θ = t_0/cos θ (1) where θ is the shearing angle of the tow. Consequently the thickness of a ply may locally increase by a factor of 4 if the fibre tow is sheared through an angle of 75°, the effects of which are currently unaccounted for in buckling optimisation studies. Furthermore, since composite laminates are more affected by transverse shear effects than isotropic materials these local areas of increased thickness make predictions of the buckling behaviour using Classical Laminate Analysis (CLA) [15] overly conservative [16,17]. Buckling optimisation algorithms using the Finite Element method (FEM) can become computationally expensive, and do not readily shed physical insight into the fundamental mechanisms in which thickness variations may enhance the buckling behaviour. For this reason a reduced 2D equivalent single-layer formulation for the flexural behaviour of VAT plate incorporating transverse shear effects was developed [18].